A 3D modeling framework for accurate trajectory-based prediction of critical diameter in deterministic lateral displacement microfluidics

Deterministic Lateral Displacement (DLD) is a high-precision microfluidic technique for particle separation based on size differences. However, the lack of an accurate predictive model for the critical diameter (Dc) limits both the design flexibility and understanding of DLD behavior. In this study, we propose a novel Dc prediction framework based on a 3D physical model, achieving high accuracy and computational efficiency. Experimental validation shows excellent agreement between predicted and actual particle trajectories. Remarkably, we discover that Dc exhibits a U-shaped variation along the vertical direction of the DLD channel, revealing a transition zone. Numerical simulations show that particles within this zone undergo vertical oscillations, causing trajectory switching between zigzag and bump modes, resulting in an altered zigzag trajectory. This framework reveals the mechanism behind altered zigzag formation from a 3D perspective and provides a powerful tool for the rapid, accurate, and customizable design of DLD microfluidic separation devices.